A complex number $z$ satisfies $z+z^*=6$, $zz^*=25$ and $\operatorname{Im}(z)0$. Find \(

Question

A complex number $z$ satisfies $z+z^*=6$, $zz^*=25$ and $\operatorname{Im}(z)>0$. Find $z$.[3] Find $z-z^*$.[1] Use the given sum and product to find $\dfrac1z+\dfrac1{z^*}$, without evaluating the two reciprocals separately.[2]

Accepted Answer

(a) $z=3+4i$ (b) $8i$ (c) $\dfrac6{25}$

Recovering a number from its sum and product

Recovering a number from its sum and product

Solution:

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